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Ab initio calculations of third-order elastic coefficients

Journal Article · · Physical Review. B
 [1];  [2];  [3]
  1. Columbia University, New York, NY (United States); OSTI
  2. Princeton University, NJ (United States)
  3. Columbia University, New York, NY (United States); Columbia University, Palisades, NY (United States)
+ Show Author Affiliations
Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an “effective” third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. Additionally, we extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.
Research Organization:
Columbia University, New York, NY (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Office of Science (SC)
Grant/Contract Number:
SC0019759
OSTI ID:
2421374
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 21 Vol. 106; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Ab initio calculations
Density functional theory
Elastic modulus
Elasticity
High-pressure studies
Materials Science
Physics
Pressure effects